Meaning of Sheaf | Babel Free

Definitions

1. A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
2. Any collection of things bound together.
3. A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
4. A quantity of arrows, usually twenty-four.
5. A sheave.
6. An abstract construct in topology that associates data to the open sets of a topological space (i.e. a presheaf) in such a way so as to make the local and global data compatible, generalizing the situation of functions, fiber bundles, manifold structure, etc. on a topological space. Formally, a presheaf ℱ whose sections are, in a technical sense, uniquely determined by their restrictions onto smaller sets: that is, given an open cover U_i of U:
7. If two sections over U agree under restriction to every U_i, then the sections are the same.
8. Given a family of sections s_i∈ℱ(U_i) such that all pairs (s_i,s_j) agree under restriction to U_i∩U_j, there is a (unique) section s over U whose restriction to U_i is s_i.

Equivalents

Examples

“O, let me teach you how to knit again / This scattered corn into one mutual sheaf, / These broken limbs again into one body.”

“Ev’n while the Reaper fills his greedy hands, / And binds the golden Sheafs in brittle bands”

“a sheaf of paper”

“Together the two men march up the aisle and mount the dais, and while Muspole shakes hands with the chairman and his lady, the major draws a sheaf of notes from a briefcase and lays them on the table.”

“The sheaf of arrows shook, and rattled in the case.”

“Arrows were anciently made of reeds, afterwards of cornel wood, and occasionally of every species of wood: but according to Roger Ascham, ash was best; arrows were reckoned by sheaves, a sheaf consisted of twenty-four arrows.”

CEFR level